Vosko-Wilk-Nusair function

Figure 2-6. Comparison of calculated and experimental vertical excitation energies of Be and H20. TDDFT is based on the Slater-Vosko-Wilk-Nusair functional. See Ref. [110] for details...

The extension of TDDFT and Tamm-Dancoff TDDFT to crystalline polymers is straightforward within the formalisms of Section 2.2.2. Figure 2-7 summarizes the results of TDDFT calculations of the photoconduction, photoemission, and optical absorption thresholds (energy gap, ionization energy, and excitation energy) of polyethylene as a function of basis set [50], The Slater-Vosko-Wilk-Nusair functional [116, 117] is used, but the following conclusion is unaltered... 

Figure 2-7. TDDFT (the Slater-Vosko-Wilk-Nusair functional) predictions of the photoconduction (fundamental gap), photoemission (ionization), and optical absorption (excitation) energies of polyethylene [50]...

Figure 2-8. Convergence of the excitation energy to the lowest-lying singlet exciton computed by CIS and TDDFT using the Slater-Vosko-Wilk-Nusair functional with the STO-3G basis set as a function of the number of wave vector sampling points (K) [50]. The error is defined as the absolute difference from the K = 100 results. The converged (K = 100) result with TDDFT is very close to the fundamental energy gap...

Here j SDA timkind of accurate pure DFT LSDA non-gradient-corrected exchange functional alluded to in section 7.2.3.4b, is the KS-orbital-based HF exchange energy functional of Eq. (7.30), is the Becke 88 exchange functional mentioned above, is the Vosko, Wilk, Nusair function (VWN, or Slater VWN, SVWN... 

The role of crystal symmetry properties in determining the shape of the bands has been emphasized, but the few examples reported have also shown that the existence of a gap and the energy range of bands depend on the mutual interactions of all particles, electrons, and nuclei, in the lattice. Therefore, the correctness of a calculation is largely dependent on the kind of approximation used in the evaluation of such interactions. In fact, different approximations of the Hamiltonian can produce a variety of results and, in particular, band structures that are not only quantitatively but also qualitatively different in some cases. In Figure 18, the HF band structure of silicon is compared with that obtained with DFT methods, both in the LDA, in the form of Slater-Vosko-Wilk-Nusair ° functional, and with the Becke 3 (B3) parameter-Lee-Yang-Parr (LYP) approximation, which incorporates a part of the exact exchange... 

The Xa method is an example of LDA in which the correlation energy is neglected and the exchange energy expression is multiplied by a parameter a. A fairly accurate expression for the correlation energy of the uniform electron gas, the VWN (Vosko, Wilk, Nusair) functional, was derived by fitting it to Monte Carlo results. 

CSM = continuum solvation model COSMO = conductorlike screening model COSMO-RS = generalization of COSMO to real solvents QC = quantum chemical PCM = polarizable continuum model SAS = solvent accessible surface SES = solvent excluding surface NPPA = average number of segments per full atom vdW = van der Waals, VWN = Vosko-Wilk-Nusair functional (see Density Functional Theory Applications to Transition Metal Problems). 

SVWN Model. (Slater, Vosko, Wilk, Nusair) A Density Functional Model which involves the Local Density Approximation. 

VWN5 A Vosko, Wilk, Nusair correlation functional... 

Hedin- Lundqvist, HL, exchange-correlation potential [37], which is equivalent to our earlier use [130] of the von Barth-Hedin potential, vBH, [38] with parameter values as used by Hedin and Lundqvist. Calculations were also performed using the Xa form, with a = 0.7 [4] and the Vosko-Wilk-Nusair form of Vxc [41]. A somewhat lower total energy was obtained by inclusion of the 3d, and in particular the 3p and 3d, basis functions, compared with the results obtained using the minimal basis set. 

To confirm the minimum point of the total energy profile with respect to the U=0 distance, other exchange - correlation potentials were also examined a local density functional by Vosko-Wilk-Nusair (VWN) (14) and a nonlocal... 

The one-electron Kohn-Sham equations were solved using the Vosko-Wilk-Nusair (VWN) functional [27] to obtain the local potential. Gradient correlations for the exchange (Becke fimctional) [28] and correlation (Perdew functional) [29] energy terms were included self-consistently. ADF represents molecular orbitals as linear combinations of Slater-type atomic orbitals. The double- basis set was employed and all calculations were spin unrestricted. Integration accuracies of 10 -10 and 10 were used during the single-point and vibrational frequency calculations, respectively. The cluster size chosen for Ag or any bimetallic was... 

GGA functionals. Slater (S) exchange [68] and Vosko-Wilk-Nusair (VWN) correlation [74] LDA functionals, and the HF exchange integral with three parameters ... 

Theoretical work on the oxidation reactions of aromatic hydrocarbons is scarce. Bartolotti and Edney [10] used a simple density functional approach with the local exchange correlation functional developed by Vosko-Wilk-Nusair [11] to identify potential intermediates produced in the OH addition initiated atmospheric photooxidation of toluene. Although their energy results were acknowledgely preliminary in nature, their calculations were able to confirm certain aspects of the proposed reaction mechanism [2,3] and to predict the importance of carbonyl compounds containing... 

Any exchange functional can be combined with any correlation functional. For example, the notation BLYP/6-31G denotes a DF calculation done with the Becke 1988 exchange functional and the Lee-Yang-Parr correlation functional, with the KS orbitals expanded in a 6-31G basis set. The letter S (which acknowledges Slater s Xa method) denotes the LSDA exchange functional (15.140). VWN denotes the Vosko-Wilk-Nusair expression for the LSDA correlation functional (actually, these workers gave two differ-... 

Kafafi devised the hybrid K2-BVWN (standing for Kafafi 2-parameter, Becke, Vosko-Wilk-Nusair) exchange-correlation functional [S. A. Kafafi, /. Phys. Chem. A, 102,10404 (1998)]. K2-BVWN/6-311+G(2df) calculations of of 350 species had... 

From Reference 13, triple-J + polarization basis set for heavy atoms, double- + polarization basis set for hydrogen atoms. Vosko-Wilk-Nusair LSDA XC functional. Gradient-corrected Perdew— ng exchange and Perdew correlation functionals. 

Gradient-corrected Becke exchange and Perdew correlation functionals used perturbatively with self-consistent Vosko—Wilk—Nusair LSDA densities. 

From Reference 75, double- plus polarization basis set. Vosko-Wilk-Nusair LSDA functional. 

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